Is there a mathematical ecuation or some method, which allows you to have the "current dollar value" of an amount dollar from other year, let's say, decades ago? For example, it's said that the Marshall Plan where United States gave 13 billions dollars to Europe is equivalent to $130 billion in current dollar value as of June 2016.

3 Answers
3

You just use the inflation rate. To go forward in time take the dollar value and multiply it by (1 + inflation)

Lets say inflation in 2015 was 2% (i.e. 0.02).Then 100 USD in 2015 are equivalent to 102 USD (=100*1.02) in 2016. Suppose inflation in 2016 was 3%. Then 100$ in 2015 are equivalet to 105.06 USD in 2017 (100*1.02*1.03). Or to go back in time divide by 1+inflation rate. So 100 USD in 2017 are equal to 100/1.03 dollars in 2016.

If you have all the inflation rates and keep going, then you can figure the historical amounts out.

Saying how much a dollar was "worth" at a past point, however, is not a very precise question unless it's made more specific. The price of computers, for example, have fallen even as they have become more powerful -- and even as the price level has risen. It's simply not accurate to say that a five-hundred-sixty-three dollar computer today (of which there are many choices) would have cost only $1 in 1774!

The best way to track inflation is to look at the CPI of a country. CPI measures the price of a basket of goods across a period of time normalized to 100 (In the US it is currently normalized to 1982).

This means that in 2007 the CPI will be 100. For every other year it shows the difference between the value of a basket of goods as compared to the value in 1982. For example the CPI in the U.S. for June of 2016 was 240. this means that the value of a dollar in 1982 was 2.4x more valuable than the value of a dollar in 1982.

To compare years that are not the base year you simply find the % difference between the two CPIs. So in March 1948 (right before the Marshall Plan began) the CPI was 23.4. You use the % change formula ((new-old)/old) to calculate the % difference between the CPI in 1948 and now. Thus:

(240-23.8)/23.4 = 9.239

Thus the amount of money spent on the Marshall plan is worth 9.239 times now what it would be in 1950. Thus you can just multiply the amount spent on the Marshall Plan by the dollar value today to get:

$13 billion * $9.239 billion = $120.107 billion

It says on Wikipedia that the Marshall Plan cost more than $13 billion so to get the $130 billion number the total spent would have been just under $14 billion.

I'm not sure which year's CPI they're measuring in your statistic to value the money spent on the Marshall plan or the exact methodology used but this gets you a pretty good rough estimate.

$\begingroup$According to what criteria is the basket of goods determined? As David Croson pointed out, computers would not be a good choice because their price has fallen over the years. What are properties of goods that make them suitable for being in this basket?$\endgroup$
– GiorgioMay 29 '18 at 18:52